重质量区与超重区核素的 衰变一直是核物理领域的重要研究课题。原子核 衰变半衰期的理论研究对于探索原子核结构、鉴别新核素的合成等方面有着重要意义。本文围绕核素 衰变开展了两方面的研究工作，包括：1、基于机器学习中的贝叶斯神经网络方法研究核素的 衰变半衰期。2、基于一种对 WKB势垒贯穿几率做近似处理的公式，通过 衰变反应中母核的衰变能与半衰期，提取重质量区与超重区核素的核电荷半径。主要研究内容如下：一、基于机器学习中的贝叶斯神经网络方法（BNN）研究原子核的 衰变半衰期。（1）研究了贝叶斯神经网络方法对不同模型的修正程度，且模型按同位旋 分区和角动量 分区的方式分为两类。研究发现，BNN 方法能够在一定程度上提高模型的计算精度，且在一些偏差较大的区域，半衰期结果得到了较好的修正。（2）按角动量分区时，研究了按 =0、=1、=2、=3、=4 与 =5 六个分区内，BNN 方法对几种模型的修正程度。研究发现，BNN 方法对输入量包含 的几种模型的修正效果更明显，且奇数分区的修正程度明显大于偶数分区。（3） 对 MYQZR 模型（The modified Yibin . formula），研究了 与 两种分区方式以及不同输入量对模型提升度的影响。研究发现， 与 两种分区方式对模型的修正程度影响不大，总均方根偏差的提升度均在 23.5% 左右，基本可以忽略不计。在加入输入量 后，BNN 对模型的修正程度明显增加，说明输入量 的影响更大。

二、基于一种对 WKB 势垒贯穿几率做近似处理的公式，通过 衰变反应中母核的衰变能与半衰期，提取核素的核电荷半径。（1）通过计算将 衰变半衰期理论计算中的同位旋效应传递到 的计算结果中。验证了方法的可行性，讨论了同位旋效应在 计算结果中的影响。研究发现，同位旋效应在 SLB（The scaling law of Brown formula）与 MSLB（The modified scaling law of Brown formula）这对公式中的影响最为显著，尤其在同位旋较大的区域。（2）预言了近年来合成重质量区核素的 ，讨论了 Np、Cm 两条同位素链的计算结果。研究发现，计算结果整体趋势符合 与 ^1/3 成正比的关系。（3）系统预言并讨论了超重核素的 ， 以及 Rf、Mt、Rg 与 Cn 四条同位素链的计算结果。对于计算的核电荷半径结果，将其与微观理论模型中的相对论连续谱 Hartree-Bogoliubov 理论（RCHB）的计算结果进行对比。得到的结果比 RCHB模型更能体现原子核的奇偶效应。当利用实验衰变数据提取核电荷半径时，实验的误差会对 的计算结果产生一定影响。

The decay of heavy nuclei and superheavy nuclei has always been an important research topic in the field of nuclear physics. The theoretical study of the half-life of nuclear decay has made an important contribution to the exploration of nuclear structure and the identification of the synthesis of new nuclides. In this paper, two aspects of research work are carried out based on the decay of nuclides, including: 1. The decay half-lives of nuclides are studied based on the Bayesian neural network method (BNN). 2. Based on a formula derived from the approximation of the WKB barrier penetration probability, the nuclear charge radii of heavy and superheavy nuclides are extracted by the decay energy and half-life of the parent nucleus in the decay. The specific research contents are as follows:

Firstly, based on the Bayesian neural network method in machine learning, the decay half-life of atomic nuclei is studied. (1) The correction degree of the BNN method to different models is studied, and the models are divided into two categories according to the isospin partition and the angular momentum partition. It is found that the BNN method can improve the calculation accuracy of the model to a certain extent, and the half-life results are well corrected in some regions with large deviations. (2) According to the angular momentum partition, the correction degree of the BNN method to several models in six partitions of =0, =1, =2, =3, =4, and =5 is studied. It is found that for several models with input containing , the BNN method has a more obvious degree of correction to the model, and the degree of correction in odd partitions is significantly greater than that in even partitions. (3) Through the discussion of the MYQZR model, it is found that the two partition methods of and have little effect on the correction degree of the model, and the improvement degree of the total root mean square deviation is about 23.5%, which can be ignored. After adding input , the correction effect of BNN on the model is significantly increased, indicating that the input has a greater impact on the correction of the model.

Secondly, based on an approximate formula for the WKB barrier penetration probability, the nuclear charge radii are extracted by the decay energy and half-life of the parent nucleus in the decay. (1) The isospin effect in the theoretical calculation of decay half-life is transferred to the nuclear charge radius result by the formula. The feasibility of the method is verified, and the influence of the isospin effect on the calculated nuclear charge radius is discussed. It is found that the isospin effect is the most significant in the SLB and MSLB formulas, especially in the region with larger isospin. (2) The nuclear charge radius of nuclides in the heavy mass region synthesized in recent years is predicted, and the calculation results of Np and Cm isotope chains are discussed. It is found that the overall trend of the prediction results is in line with the relationship between and ^1/3. (3) The nuclear charge radius of superheavy nuclei and four isotope chains (Rf, Mt, Rg, and Cn) are systematically predicted and discussed. For the predicted nuclear charge radius results, we compare them with the calculation results of the RCHB model and find that the extracted by the formula can better reflect the parity effect of the nucleus than the RCHB model. It is also found that when is extracted from experimental decay data, the experimental error will have a certain impact on the prediction results of .